What is the tangent of x^3-3x^2+x-5 ?

The tangent of x^3-3x^2+x-5 is y=(3a_{0}^2-6a_{0}+1)x-2a_{0}^3+3a_{0}^2-5

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tangent of x^3-3x^2+x-5

tangent of

x^{3} - 3 x^{2} + x - 5

y = (3 a_{0}^{2} - 6 a_{0} + 1) x - 2 a_{0}^{3} + 3 a_{0}^{2} - 5

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{3} - 3 a_{0}^{2} + a_{0} - 5)

Find the slope of

y = x^{3} - 3 x^{2} + x - 5 : \frac{d y}{d x} = 3 x^{2} - 6 x + 1

Compute the slope of

y = x^{3} - 3 x^{2} + x - 5

x = a_{0} : m = 3 a_{0}^{2} - 6 a_{0} + 1

Find the line with slope m=

3 a_{0}^{2} - 6 a_{0} + 1

and passing through

(a_{0}, a_{0}^{3} - 3 a_{0}^{2} + a_{0} - 5) : y = (3 a_{0}^{2} - 6 a_{0} + 1) x - 2 a_{0}^{3} + 3 a_{0}^{2} - 5

y = (3 a_{0}^{2} - 6 a_{0} + 1) x - 2 a_{0}^{3} + 3 a_{0}^{2} - 5

\frac{\partial}{\partial x} (x^{3} + k y^{2} - 5 x y)

\int 3 x 1 - x^{2} d x

4 x y^{^{'}} = 2 x e^{x} - 4 y + 6 x^{2}

\int x sin^{3} (x^{2}) cos (x^{2}) d x

\frac{d y}{d x} = x, y (11) = 5

What is the tangent of x^3-3x^2+x-5 ?
The tangent of x^3-3x^2+x-5 is y=(3a_{0}^2-6a_{0}+1)x-2a_{0}^3+3a_{0}^2-5